Fractal interpolation surfaces and a related 2-D multiresolution analysis (Q1260885)

The concept of self-affine fractal interpolation surfaces which was given by \textit{P. R. Massopust} [J. Math. Anal. Appl. 151, No. 1, 275-290 (1990; Zbl 0716.28007)] for triangular domains, is extended to polygonal domains and arbitrary interpolation points. The concept uses so called fractal interpolation functions. An algorithm is described. A class of invariant measures supported on these surfaces is introduced and discussed as well as the fractal dimension of some simple surfaces. Using these surfaces the authors construct a sequence of nested subspaces forming a generalized multiresolution analysis.